What shape does the distribution make? 1 2 2 3 3 3 3 4 4 5
a. positive skew
b. negative skew
c. symmetrical
A teacher gives a 20- point quiz to 10 students. The scores are listed below. What percentile corresponds to the score of 12? 20, 8, 10, 7, 15, 16, 12, 19, 12, 9
a. 50
b. 12
c. 13
d. 25
To determine the shape of a distribution, you can create a histogram or a frequency distribution table. However, in this case, since the data set is small and relatively simple, you can just examine the values to determine the shape.
For the first question:
The given data set is: 1, 2, 2, 3, 3, 3, 3, 4, 4, 5
Based on the values in the data set, we can observe that there are more values on the higher end (4 and 5) and fewer values on the lower end (1 and 2). This indicates that the distribution is positively skewed.
Therefore, the answer is a. positive skew.
For the second question:
The scores are: 20, 8, 10, 7, 15, 16, 12, 19, 12, 9
To determine the percentile of a particular score, you need to calculate the percentile rank.
First, arrange the scores in ascending order: 7, 8, 9, 10, 12, 12, 15, 16, 19, 20
Next, calculate the rank (position) of the score you're interested in. In this case, the score is 12, and it appears in the 5th and 6th position.
Now, use the formula to calculate percentile rank:
Percentile Rank = (Rank / (Total number of scores - 1)) x 100
Percentile Rank = (5 / (10 - 1)) x 100 = (5 / 9) x 100 = 55.56
Therefore, the score of 12 corresponds to the approximately 55.56th percentile.
Thus, the answer is not provided in the options.